# Ancestor regression in linear structural equation models

arXiv: https://arxiv.org/abs/2205.08925 · HTML: https://mlsanity.com/paper/2205.08925/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2022.

## Built on by (most cited first, 1 of 1)

- [Tensor-based second-order causal discovery](https://mlsanity.com/paper/2606.18074/) (2026)

## Abstract (arXiv)

We present a new method for causal discovery in linear structural equation models. We propose a simple ``trick'' based on statistical testing in linear models that can distinguish between ancestors and non-ancestors of any given variable. Naturally, this can then be extended to estimating the causal order among all variables. We provide explicit error control for false causal discovery, at least asymptotically. This holds true even under Gaussianity, where other methods fail due to non-identifiable structures. These type I error guarantees come at the cost of reduced empirical power. Additionally, we provide an asymptotically valid goodness of fit p-value to assess whether multivariate data stems from a linear structural equation model.